by Douglas Robson, USA TODAY Sports

by Douglas Robson, USA TODAY Sports

NEW YORK - Down two sets to Gael Monfils in Thursday night's U.S. Open quarterfinals, Roger Federer sat in his changeover chair.

The match was slipping away. At 33, and with his career-long foil Rafael Nadal sidelined, so was one of Federer's best chances to add to his record haul of 17 majors.

But this is not how a champion thinks, no matter how contradictory it must sound looping through a brain trying to process reality.

"I still thought the finish line was far for Gael," recalled Federer.

And then, the second-seeded Swiss orchestrated his most daring comeback, saving two match points in the fourth set to defeat 20th-seeded Monfils 4-6, 3-6, 6-4, 7-5, 6-2 in front of a thrilled Arthur Ashe Stadium crowd.

It was Federer's ninth comeback from two sets down and his first win facing match points at a major, according to the ATP Tour. It also sent him to the U.S. Open semifinals for the first time since 2011.

Federer's escape was helped, of course, because Monfils, the crowd-pleasing Frenchman enjoying a renaissance of his own, has a history of self-destructing. But until the final set, he defied a patchy past and held his own.

Despite a 25-1 record under the lights on Arthur Ashe Stadium, Federer came out flat for the first two sets.

Monfils, playing measured and contained counter-punching tennis, provided few theatrics.

There were a few signature antics - pretending to give up after a poor drop-shot and then hitting a volley to win the point; leaping for an overhead and changing his mind and letting it bounce (it was out); and rolling his right ankle early in the second set and getting away with a successful challenge while still laying on the court in pain.

But the 28-year-old Frenchman recovered from early breaks in the third and fourth sets before wilting under the weight of his missed opportunity in the final set.

"I had a little drop," Monfils said of his mental and physical lapse. "Roger just jumped on me."

To win a sixth U.S. Open, Federer will have to rely on something besides his logic-defying grit: His volley.

Against Monfils, Federer went to the net a whopping 74 times - almost double his average of 40 in his first four matches. The tactic worked: He won 72% of them, and 79% of his serve-and-volley points, too.

Federer, like most of his peers, has made baseline play his provenance in an era when defense rules and spin-friendly rackets have made passing shots particularly deadly.

But under the tutelage of his boyhood idol, Stefan Edberg, who he hired to help coach him this season, Federer has increasingly returned to the net-charging days of his early professional career.

The Swiss actually said he didn't come in enough against Monfils, but explained that he might not venture forward as much against less patient opponents.

"I'm happy I kept on pressing, and that I got a reward for it tonight," he said.

He might need some luck, too.

Monfils wasn't in control of either match point when Federer fell behind 15-40 on his serve at 4-5 in the fourth set.

But he had a look at the first one, sending a backhand passing shot long when Federer did too little with a volley.

At that point, reason set in.

"I thought,, 'This is it,' " Federer said in an on-court interview. "This is the last point, man. Just go down fighting. Don't miss an easy shot."

Federer fought, and lived, and now he has a chance - as illogical as it seems - to put his mind to work on another Grand Slam title.